Photometry for Traffic Engineers...

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Marvin Cobb
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1 Photometry for Traffic Engineers... Workshop presented at the annual meeting of the Transportation Research Board in January 2000 by Frank Schieber Heimstra Human Factors Laboratories University of South Dakota Many figures borrowed from: Ryer, A. Light Measurement Handbook. (An excellent and practical resource!!!) TRB 2000 Photometry for Traffic Engineers 1

2 Basic Light Measurement Visible Electromagnetic Radiation (Light) Radiometric to Photometric Conversion Luminous Flux (Lumens) Luminous Intensity (Candela) Illuminance (Lux) Luminance (cd/m 2 ) TRB 2000 Photometry for Traffic Engineers 2

3 Taxonomy of Photometric Units Luminous Flux Lumen Total effective output of a lamp Luminous Intensity Candela Light density through space Vehicle headlamps Traffic signal lamps/lenses Illuminance Lux Light density falling upon a surface Roadway illumination Highway sign illumination Luminance Candela/m 2 Brightness of extended source/surface Highway sign brightness/contrast Proxy for retroreflectivity TRB 2000 Photometry for Traffic Engineers 3

4 Light Energy Light is visible electromagnetic radiation Magnitude measured in Watts (1/746 H.P.) Wavelength (l): 380 to 730 nm ( nominal) Frequency: 789 down to 384 THz l TRB 2000 Photometry for Traffic Engineers 4

5 Relative Luminous Efficiency CIE Spectral Luminosity Function Dark Adapted V l V l Wavelength (nm) Light Adapted 700 The human eye is more sensitive to some visible wavelengths than others Measurements of light must take these effects into account CIE V l curve corrects for the differences across wavelengths TRB 2000 Photometry for Traffic Engineers 5

6 Commission Internationale de l Eclairage (CIE) V l (Color Plate) TRB 2000 Photometry for Traffic Engineers 6

7 Lumens per Watt Radiometric to Photometric Conversion via CIE V l and V l lm/w 683 lm/w Scotopic (V l ) Dark Adapted Peak l = 507 nm K m = 1700 lm/w 2.5 X Sensitivity Wavelength (nm) 700 Photopic (V l ) Light Adapted Peak l = 555 nm K m = 683 lm/w TRB 2000 Photometry for Traffic Engineers 7

8 Luminous Flux (The Lumen) TRB 2000 Photometry for Traffic Engineers 8

9 Luminous Flux Luminous Flux is the photometrically (V l ) corrected equivalent of the Watt 1 Lumen = 1/683 Watts at 555 nm (peak V l ) Luminous Flux in lumens is calculated as: e,l V(l) dl TRB 2000 Photometry for Traffic Engineers 9

10 Luminous Flux Equation Revealed Lumens per Watt Conversion Factor for CIE V l Curve Lumens = Radiant Energy in Watts e,l V(l) dl Wavelength Sampling Increment Integrate over Visible Spectrum CIE Spectral Luminosity Function TRB 2000 Photometry for Traffic Engineers 10

11 Step-by-Step Calculation of Luminous Flux Measure radiant energy (Watts) from light source at each l across the visible spectrum ( nm) Convert Watts to Lumens via the V l curve and the photopic maximum luminous efficiency constant (683 lm/w at 555 nm) Integrate Lumens across visible spectrum TRB 2000 Photometry for Traffic Engineers 11

12 Step 1. Measure Radiant Energy across l using a Spectroradiometer Light Watts per nm Precision Aperture and Optics Diffraction Grating Photodiode Array MUX (See next slide for sample data) Current Amplifier TRB 2000 Photometry for Traffic Engineers 12

13 Watts per nm Sample Data from Spectroradiometer Radiant Flux (Watts) measured every 10 nm from nm Wavelength (nm) TRB 2000 Photometry for Traffic Engineers 13

14 Watts per nm Relative Luminous Efficiency Lumens per Watt Step 2. Convert Watts to Lumens X = Wavelength (nm) Wavelength (nm) 0 (See next slide for results) TRB 2000 Photometry for Traffic Engineers 14

15 Lumens per nm Results of V l Conversion Wavelength (nm) 800 TRB 2000 Photometry for Traffic Engineers 15

16 Lumens per nm Step 3. Integrate Lumens from nm Wavelength (nm) 800 Integration across the visible spectrm yields a Luminous Flux measurement of 2890 Lumens TRB 2000 Photometry for Traffic Engineers 16

17 Luminous Flux Equation Revisited Lumens per Watt Conversion Factor for CIE V l Curve Lumens = Radiant Energy in Watts e,l V(l) dl Wavelength Sampling Increment Integrate over Visible Spectrum CIE Spectral Luminosity Function TRB 2000 Photometry for Traffic Engineers 17

18 Luminous Intensity (The Candela) TRB 2000 Photometry for Traffic Engineers 18

19 Luminous Intensity (Power of Directional Beams) Luminous Intensity refers to the amount of luminous flux emitted into a solid angle of space in a specified direction (since many sources are not isotropic) The SI unit of Luminous Intensity is the candela The candela is historically linked to candle power (ie., 1/683 W/sr at 555 nm) 1 candela = 1 lumen unit solid angle steradian TRB 2000 Photometry for Traffic Engineers 19

Solid Angles, Surfaces of Spheres Imaginary Sphere Surrounding a point source of light and the Steradian Steradian (w) = Area r 2 Area 1 m 2 subtends 1 sr at a distance of 1 m since w = A

20 Solid Angles, Surfaces of Spheres Imaginary Sphere Surrounding a point source of light and the Steradian Steradian (w) = Area r 2 Area 1 m 2 subtends 1 sr at a distance of 1 m since w = A 1 m = 2 r 2 = 1 1 m 2 Sphere Area = 4pr 2 r ie., distance Surface area of a sphere is subtended by 4p sr w = A = 4pr 2 = TRB 2000 Photometry for Traffic Engineers 20 r 2 r 2 4p = p

21 The Candela An isotropic light source with a luminous intensity of 1 cd is emitting a total luminous flux of approximately 4p lumens (since an isotropic source emits light into a total volume of 4p sr) TRB 2000 Photometry for Traffic Engineers 21

22 Broadband Measurement of Luminous Intensity Precision Aperture (e.g., 1 cm 2 ) CIE V l Filter Silicon Photodetector Display r = 50 cm Current Amplifier Photometer aperture subtends sr at 50 cm distance ( w = Area / r 2 = 1 cm 2 / (50 cm) 2 = sr ) Light energy in sr is filtered and converted to current Current is converted to lumens (per calibration constant) Lumens divided by sr = Candelas ( e.g., lm / sr = lm/sr (candelas) ) TRB 2000 Photometry for Traffic Engineers 22

23 Illuminance (Lux) TRB 2000 Photometry for Traffic Engineers 23

24 Illuminance The photometrically corrected light energy falling upon a given unit of surface area (e.g. lumens/m 2 ) 1 foot 1 meter cd = 1 m 2 at distance of 1 m subtends 1 steradian 1 lumen per m 2 = 1 lux 1 ft 2 at a distance of 1 ft subtends 1 sr (w = 1 ft 2 / 1 ft 2 = 1 steradian) 1 cd source emits 1 lumen into 1 sr 1 lumen per ft 2 = 1 foot-candle (fc) 1 ft 2 = m 2 The foot-candle contains times more light per unit area than the lux TRB 2000 Photometry for Traffic Engineers 24

Inverse-Square Law Since light from a point source expands outward, illuminance available to a surface decreases according to the inverse-square law An illuminaire can be

25 Inverse-Square Law Since light from a point source expands outward, illuminance available to a surface decreases according to the inverse-square law An illuminaire can be treated as a point source when the viewing distance is at least 5X greater than the diameter of the light source (5-to-1 rule) TRB 2000 Photometry for Traffic Engineers 25

26 Inverse-Square Law Example E = I/d 2 cos( ); E 1 d 1 2 = E 2 d 2 2 where: E = illuminance (lux) d = distance (m) I = luminous intensity (candelas) d 1 = 1 meter 1 m 2 1 m 2 d 2 = 2 meters E 2 = E 1 d 12 /d 2 2 = E 1 * 1 2 /2 2 = E 1 /4 Double the distance, Quarter the energy TRB 2000 Photometry for Traffic Engineers 26

27 Cosine Law Illuminance also decreases with the angle of incidence, as captured by the cosine law E = cos( ) * E 0 where: E = Illuminace resulting from light incident at an angle degrees from the normal E 0 = Illumination resulting from light incident perpendicular (normal) to the surface plane TRB 2000 Photometry for Traffic Engineers 27

28 Cosine Law Example = 0-deg = 30-deg = 60-deg E = cos(0) * E 0 E = 1.0 * E 0 E = cos(30) * E 0 E = 0.86 * E 0 E = cos(60) * E 0 E = 0.50 * E 0 As the angle of incidence increases from 0-degrees (from the normal) to 90-deg, the light density falling upon a surface drops by a factor of cos( ) TRB 2000 Photometry for Traffic Engineers 28

29 Broadband Photometer (Illumination Meter) Precision Aperture Silicon Photodetector Light Display Lux Cosine Diffuser CIE V l Photometric Correction Filter Current Amplifier TRB 2000 Photometry for Traffic Engineers 29

30 Cosine Diffuser Head Cosine Diffuser Precision diffusion lens can redirect off-axis light toward the detector while also effectively applying the cosine correction factor TRB 2000 Photometry for Traffic Engineers 30

31 Luminance (lux/sr x 1/m 2 ; candela/m 2 ) TRB 2000 Photometry for Traffic Engineers 31

32 Luminance is a measure of the: Luminance luminous flux density per beam solid angle areal density of luminous intensity emitted from an extended source luminous intensity of the projected image of an extended source per unit area of that extended source The SI unit of luminance is the candela per m 2 ( nit ) TRB 2000 Photometry for Traffic Engineers 32

33 Luminance as Projected Luminous Intensity Luminous intensity (cd = lm/sr) L di cd/m 2 = da * cos( ) Projected Area (m 2 ) Luminous Surface Area (A) TRB 2000 Photometry for Traffic Engineers 33

34 Luminance is an Abstraction Luminance is not a source quantity nor a detector quantity; instead, it is a purely geometric quantity that describes the beam of light (areal image) connecting the source and the detector. An optical system (e.g., eye or photometer) is needed to convert luminance into an illuminance at the detector (e.g., retinal illuminance or trolands ). Luminance is useful insofar as it correlates fairly well with the psychophysical dimensions of brightness and contrast. TRB 2000 Photometry for Traffic Engineers 34

35 Broadband Luminance Meter Eyepiece Condenser Lens CIE V l Correction Filter Focusing Lens Mirror Precision Aperture Silicon Photodetector TRB 2000 Photometry for Traffic Engineers 35

36 Conservation of Luminance Across Viewing Geometry Lambert s Law of Surface Diffusion Angle of Observation Observation Distance TRB 2000 Photometry for Traffic Engineers 36

37 Lambertian Surface Diffusion (Another Cosine Law) Incident Beam cos(0)=100% cos(30)=87% Lambertian Transmittance cos(60)=50% Lambertian Reflectance Incident Beam TRB 2000 Photometry for Traffic Engineers 37

Observation Angle Surface area sampled through a given aperture size increases as a factor of cos( ) 0-deg 60-deg Bird s eye view 0-deg 0-deg 60-deg However, this increase

38 Observation Angle Surface area sampled through a given aperture size increases as a factor of cos( ) 0-deg 60-deg Bird s eye view 0-deg 0-deg 60-deg However, this increase in surface area is offset by the fact that the emission of light from the area being sampled decreases by the same factor of cos( ) TRB 2000 Photometry for Traffic Engineers 38

39 Observation Distance Luminance in independent of viewing distance to an extended source since the sampled area (FOV) increases with distance is a manner that cancels-out concurrent inverse-square losses. Caveat: The extended source must completely fill the aperture of the mesurement device! TRB 2000 Photometry for Traffic Engineers 39

40 Special Problems: LED Symbol Heads How do you obtain a useful photometric field quantity to characterize LED-based symbol signs? TRB 2000 Photometry for Traffic Engineers 40

41 Light Emitting Diodes (LED s) What other problems do LED s present regarding their photometric characterization? TRB 2000 Photometry for Traffic Engineers 41

42 References DeCusatis, C. (Editor). Handbook of Applied Photometry. New York: Springer-Verlag, [Am. Inst. Physics] Ryer, A. Light Measurement Handbook. Photometry for Traffic Engineers Web Page TRB 2000 Photometry for Traffic Engineers 42

Photometry for Traffic Engineers...

Photometry for Traffic Engineers... Workshop presented at the annual meeting of the Transportation Research Board in January 2000 by Frank Schieber Heimstra Human Factors Laboratories University of South